基于零测度集刻画函数黎曼可积性  

Describing Function Riemannian Integrability Based on Zero Measure Set

作　　者：张安玲[1] Zhang An-ling(Department of mathematics Changzhi University,Changzhi Shanxi 046000)

机构地区：[1]长治学院数学系,山西长治046000

出　　处：《长治学院学报》2021年第5期1-6,共6页Journal of Changzhi University

基　　金：山西省教育厅教改项目(J2020320);山西省教育厅教改项目(J2018180)。

摘　　要：函数的黎曼可积性在数学分析中具有重要作用,判断函数的黎曼可积性也是数学分析中的一个难点。文章从函数在区间上不连续点成一零测度集这一角度去判断函数的黎曼可积性,为判断函数的黎曼可积性提供了一种简便实用的方法。利用该方法解决了一些数学分析中关于黎曼可积性的问题,使该问题简单化且容易理解。The Riemann integrability offunction plays a very important role in mathematical analysis.It is also a difficult point to judge the Riemann integrability of function.In this paper,the Riemannian integrability of function is judged from the point of view that the discontinuous points of the function on the interval form a set of zero measures.This paper provides a simple and practical method for judging the Riemann integrability of functions.This method is used to solve some problems about Riemann integrability in mathematical analysis,making it simple and easy to understand.

关 键 词：黎曼可积性 零测度集 间断点 可数集 

分 类 号：O172.2[理学—数学]